Virtual temperature measuring point

ABSTRACT

The invention relates to a method for determining a temperature profile and the integral mean temperature and/or axis temperature in a thick wall or shaft. In order to determine a mean integral wall temperature during heating or cooling processes in a multilayer model, the mean integral wall temperature is calculated from the mean temperature of each layer. A multilayer model is used for determining the mean integral wall temperature during heating or cooling processes and draws upon the mean temperature of each layer.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is the U.S. National Stage of International ApplicationNo. PCT/EP2006/066704, filed Sep. 25, 2006 and claims the benefitthereof. The International Application claims the benefits of Europeanapplication No. 05022820.4 filed Oct. 19, 2005, both applications areincorporated by reference herein in their entirety.

FIELD OF INVENTION

The invention relates to a method for determining the temperatureprofile and the average integral temperature and/or axial temperature inwalls or shafts of thick-walled components, such as for example of steamcollectors, steam lines, valve housings, turbine housings or shafts orthe like.

BACKGROUND OF THE INVENTION

During heating-up and cooling-down processes, as occur in componentwalls, for example in a steam turbine, a valve housing or a steam line,in particular when changing the operating mode, temperature gradientsare produced in thick walls of these components and may lead toconsiderable material stresses. These material stresses may lead topremature material wear to the extent that cracks form.

To monitor such temperature gradients specifically in the case ofapplications in steam power plants, previously at least one or moretemperature measuring points were incorporated in the component wall.Measured values determined for the temperature of the wall and thetemperature of the working medium can be used to estimate temperaturedifferences within the component wall and in particular to determine theassigned average integral wall temperature. Comparison of the averageintegral temperature with permissible limit values makes it possible tokeep the thermal material stresses within permissible limits. However,this method is comparatively cost-intensive and error-prone.

Alternatively, the average integral wall temperature can also becalculated without the need for costly and error-prone measuring pointsincorporated in the wall or in the case of components which cannot beprovided with a measuring point (for example a turbine shaft). Onepossible method is to calculate this temperature by means of amathematical substitute model, in particular on the basis of the Besselequation, for the heat conduction in a metal rod. However, systemspreviously realized on this basis in the instrumentation and control ofindustrial plants, such as for example tubes of steam power plants, havea tendency to undergo oscillations, dependent on the period of thetemperature changes of the working medium, which limit reliableassessment of the temperature values obtained in such a way.

SUMMARY OF INVENTION

The invention is therefore based on the object of providing a method fordetermining the average integral wall temperature/axial temperaturewhich produces a particularly accurate picture of the temperatureprofile, and at the same time is particularly robust and intrinsicallystable, without the use of temperature measuring points in the wallconcerned.

This object is achieved according to the invention by using a multilayermodel based on the average temperature of each layer for determining theaverage integral wall temperature during heating-up or cooling-downprocesses.

When a multilayer model is used in such a way, the component wall isadditionally divided up into a number of layers lying parallel to thesurface, the number of layers depending on the wall thickness. Thematerial data used for each layer (thermal capacity, thermalconductivity) are independent of the layer geometry. A transientbalancing of the heat flows entering and leaving takes place in eachlayer. The transient heat balance obtained is used to determine thecorresponding average layer temperatures.

The multilayer model advantageously uses as measured values only theprocess variables of the steam temperature T _(AM) and steam mass flow{dot over (m)}_(AM) as well as the initial temperature profile in thewall, which in the balanced initial state can be represented by aninitial wall temperature T _(Anf). If there is no steam mass flowmeasurement, the steam throughput is calculated by means of a substitutemodel based on the pressure p_(AM) and the valve position H_(AV) or thefree flow cross section. These process variables can be easily acquiredand are generally available in any case in the instrumentation andcontrol of a technical plant. In particular, no additional measuringpoints that have to be integrated in the wall concerned are required.

The invention is based on the consideration that it is possible tocalculate the temperature profile in the wall, and consequently theaverage integral wall temperature, during heating-up and cooling-downprocesses sufficiently accurately and stably by means of a multilayermodel, thereby dispensing with cost-intensive and error-prone measuringpoints incorporated in the wall and also in cases where no directtemperature measurement is possible. For this purpose, determination ofthe momentary wall temperature profile as a function of the transientheat flow balance is envisaged. In principle, it is possible to workwith the inner and outer wall surface temperatures of the thick-walledcomponent or even with the temperature of the working medium and theambient or insulating temperature or else just the surface temperature(for example in the case of a shaft).

However, it proves to be particularly favorable to divide the thickwalls up into a number of layers. A resultant advantage is betterdetermination of the wall temperature profile, and consequently bettercalculation of the average integral wall temperature, since thetransient temperature profile within a thick wall has strongnon-linearity. The reason for this is, in particular, that the thermalconductivity of the material and the specific thermal capacity of thematerial are themselves temperature-dependent. A further advantage ofthe use of a multilayer model is that, if the wall is divided upsufficiently finely into a number of layers, a forward-directedcalculation structure can be used for calculating thetemperature-dependent thermal conductivity and specific thermalcapacity, i.e. the average temperature of the preceding layer instead ofthe current layer is used, thereby avoiding feedback, which may alsohave a positive sign, and the calculation circuit thereby having a muchmore robust behavior.

The calculation of the heat transfer coefficient α preferably takesplace with allowance for the steam condensation, the wet steam and thesuperheated steam. For this, detection of the state of the workingmedium takes place in a module. Both possible condensation, with thecorresponding steam element and water element, and the superheated steamstate are detected. If superheated steam is exclusively provided as theworking medium, the heat transfer coefficient α_(AM) for the transfer ofthe heat flow from the working medium into the first layer of wall isadvantageously formed as a function of the steam throughput {dot over(m)}_(AM).

If, on the other hand, steam condensation occurs, the transfercoefficient α is advantageously calculated by a constant heat transfercoefficient α_(W) being used for the condensed element of the workingmedium, the so-called condensation component. In order to determine thiscondensation component, the saturation temperature T_(S) is used as afunction of the pressure p_(AM), the temperature T_(AM) of the workingmedium and the temperature of the heated/cooled surface T₁ (the averagetemperature of the first layer).

The temperature of the first layer of the thick-walled component T₁ issubtracted from the greater of the two values and the result is comparedwith a constant K, which can be set. The greater of these two valuesforms the divisor of two quotients, which have in the dividend thedifference between the temperature of the working medium and thesaturation temperature T_(AM)−T_(S) and the difference between thesaturation temperature and the temperature of the first layer of thethick-walled component T_(S)−T₁. The first quotient, if it is positive,is multiplied by the heat transfer coefficient α_(AM) of the superheatedsteam, the second quotient, if it is positive, is multiplied by the heattransfer coefficient α_(W) for water, in order to allow for thecondensation. The sum of the two products is compared with the heattransfer coefficient α_(AM) of the superheated steam. The greater of thetwo values is the resultant heat transfer coefficient α.

The calculation of the average integral wall temperature T _(Int) isobtained in a particularly advantageous way from a transient balancingof the entering and leaving heat flows in n individual layers. Thistakes place in n so-called layer modules.

In the first layer module, the heat flow of the working medium into thefirst layer {dot over (q)}_(AM-1) and the heat flow from the first layerinto the second layer {dot over (q)}₁₋₂ are calculated with the aid ofthe heat transfer coefficient α; the temperature T_(AM) of the workingmedium and the average temperature. With the initial temperature T_(Anf)in the layer concerned, the average temperature T₁ of the first layer isobtained by integration over time from the transient difference betweenthe heat flows of the working medium into the first layer and from thefirst layer into the second layer {dot over (q)}_(AM-1)−{dot over(q)}₁₋₂.

In a kth layer module, the average temperature of the kth layer T_(k) iscalculated with the aid of the transient heat flow balance of the(k−1)th layer {dot over (q)}_((k−1)−k) and from the kth layer into the(k+1)th layer q k-(k+1). With the initial temperature T_(Anf) _(—) _(k)of the kth layer, the average temperature T_(k) of the kth layer isobtained by integration of the transient difference between the heatflows {dot over (q)}_((k−1)−k)−{dot over (q)}_(k−(k+1)) into and fromthe kth layer over time.

In the last layer module, finally, the average temperature T₁ of thelast (nth) layer is calculated from the transient heat flow balance fromthe last-but-one (n−1)th layer into the last (nth) layer and from thelast layer into the thermal insulation {dot over (q)}_((n-1)-n)−{dotover (q)}_(n-ISOL).

The temperature dependence of the thermal conductivity λ_(k) and thespecific thermal capacity c_(k) of the kth layer is expedientlyapproximated by polynomials, preferably of the second degree, orspecified by corresponding functions.

Finally, the average integral wall temperature T _(Int) is determined ina module in a particularly advantageous way by weighting of the averagetemperatures T_(k) of the individual layers with allowance for theweight of the material of the layer and the weight of the material ofthe equivalent portion of the wall.

The entire method is preferably carried out in a specific enhanced dataprocessing system, preferably in an instrumentation and control systemof a steam power plant.

The advantages achieved with the invention are, in particular, that thewall temperature profiles and the average integral wall temperature ofthick-walled components can be reliably and stably specified alone fromthe process parameters of the mass flow and temperature of the workingmedium as well as the initial temperature distribution in the wall and,if no direct measurement of the temperature throughput is available orpossible, additionally with pressure and a valve position or a free flowcross section, thereby dispensing with measuring points incorporated inthe component walls. The greater the number of layers that is chosenhere, the more accurate the determination of the average integral walltemperature/axial temperature becomes.

BRIEF DESCRIPTION OF THE DRAWINGS

An exemplary embodiment of the invention with the use of a three-layermodel and allowance for insulation (fourth layer) is explained in moredetail on the basis of a drawing, in which:

FIG. 1 shows a section through a steam tube as an example of a thickwall divided up into three layers,

FIG. 2 shows a block diagram of the module for the calculation of theheat transfer coefficient,

FIG. 3 shows a block diagram of the module for the calculation of theaverage temperature of the first layer,

FIG. 4 shows a block diagram of the module for the calculation of theaverage temperature, of the second layer,

FIG. 5 shows a block diagram of the module for the calculation of theaverage temperature of the third layer, and

FIG. 6 shows a block diagram of the module for the calculation of theaverage integral wall temperature.

The same parts are provided with the same designations in all thefigures.

DETAILED DESCRIPTION OF INVENTION

FIG. 1 shows a tube portion 1 in section as an example of a thick wall.The interior space 2 of the steam tube is flowed through by the workingmedium (steam), and from here the heat flow is transferred into thefirst layer 4. This is followed by the second layer 6 and the thirdlayer 8. The tube portion 1 is enclosed by the insulation 10.

According to FIG. 2, the measured value of the steam throughput {dotover (m)}_(AM) is fed as the input signal to the function generator 32,which calculates from this the heat transfer coefficient α_(AM) as afunction of the working medium {dot over (m)}_(AM) for the case ofsteam, α_(AM)=f({dot over (m)}_(AM)). This function is given by a numberof interpolation points, intermediate values being formed by suitableinterpolation methods.

In order also to allow for the case of partial condensation, thepressure of the working medium p_(AM) is also passed to the input of afunction generator 34, which replicates the saturation functionT_(s)=f(p_(AM)), and consequently supplies at its output the saturationtemperature T_(S) for the respective pressure. This function is given byinterpolation points (pressures and temperatures from steam tables),intermediate values being determined by means of suitable interpolationmethods.

The temperature of the working medium T_(AM) is compared with thesaturation temperature T_(S) by the maximum generator 36. The averagetemperature of the first layer T₁ is subtracted from the greater valueby a subtractor 38. The difference is compared by means of a maximumgenerator 40 with a constant K, which can be set. Consequently, thesignalN=max(max(T _(AM) ;T _(S))−T ₁ ;K)

is present at the output of the maximum generator 40. It is passed tothe divisor inputs of two dividers 42 and 44.

The divider 42 receives at its dividend input the differenceT_(AM)−T_(S) formed by means of the subtractor 46. The functiongenerator 48 only passes on the signal

$\frac{T_{AM} - T_{XS}}{N}$

to the one input of the multiplier 50 if it is positive. The signalindicates the percentage of the working medium that is evaporated, theso-called steam component. If the difference T_(AM)−T_(S) is negative,that is to say the temperature of the working medium is lower than thesaturation temperature, the signal “zero” is present at thecorresponding input of the multiplier 50.

At the other input of the multiplier 50, the heat transfer coefficientα_(AM) for steam is present. Therefore, the heat transfer coefficientα_(pD) weighted with the steam component is passed to the one input ofthe adder 58.

The divider 44 receives at its dividend input the difference T_(S)−T₁formed by the subtractor 52. The function generator 54 only passes thesignal

$\frac{T_{S} - T_{1}}{N}$

on to the one input of the multiplier 56 if it is positive. The signalspecifies the percentage made up by the condensation component. If thedifference T_(S)−T₁ is negative, that is to say the average temperatureof the first layer is higher than the saturation temperature, the signal“zero” is present at the corresponding input of the multiplier 56.

The heat transfer coefficient α_(W) for water is present at the otherinput of the multiplier 56. Therefore, the heat transfer coefficientα_(pW) weighted with the condensation component is passed to the secondinput of the adder 59.

At the maximum generator 60, the heat transfer coefficient α_(AM) forthe case of steam is present at one input. The heat transfer coefficientα_(p)=α_(pW)+α_(pD)

for the case of partial condensation, formed by the adder 58, is presentat the second input. The greater of the two values is the current heattransfer coefficient α.

If there is no steam mass flow measurement, the steam mass flow iscalculated, for example with the aid of the following calculationcircuit. In a function generator 12, the actual value of a valveposition H_(AV) is converted into a free flow area A_(AV). The free flowarea is provided with suitable conversion factors K_(U1) and K_(U2) bymeans of multipliers 14 and 16 and passed to a further multiplier 18.The pressure of the working medium p_(AM) is passed—likewise by means ofa multiplier 20 with a suitable conversion constant K_(U4)—to the secondinput of the multiplier 18, the result of which is passed to the inputof a multiplier 22. The temperature T_(AM) of the working mediumprovided with a suitable conversion factor K_(U5) by means of amultiplier 24 is passed to the denominator input of a divider 26, thenumerator input of which receives a one. The reciprocal value is presentat the output. The root of the reciprocal value is passed to the secondinput of the multiplier 22 by means of a root extractor 28. The signalat the output of the multiplier 22, provided with a suitable conversionfactor K_(U3) by means of a multiplier 30, represents the steamthroughput {dot over (m)}_(AM). Altogether, the following isconsequently obtained for the calculation of the steam throughput:

A_(AV) = f(H_(AV))${\overset{.}{m}}_{AM} = {K_{U\; 3}*\sqrt{\frac{1}{K_{U\; 5}T_{AM}}}K_{U\; 4}T_{AM}K_{U\; 1}K_{U\; 2}{A_{AV}.}}$

The module for the first layer according to FIG. 3 determines theaverage temperature of the first layer T₁ from the transient heat flowbalance. For this purpose, the temperature difference T_(AM)−T₁ is firstformed by means of a subtractor 62 from the temperature of the workingmedium T_(AM) and the average temperature of the first layer T₁ and ismultiplied by the heat transfer coefficient α by means of a multiplier64. A multiplier 66 provides the signal with a suitable coefficientK_(AL), which can be set and represents an equivalent first surface—forthe heat transfer from the working medium into the component wall.Present at the output of the multiplier 66 is the signal for the heatflow from the working medium into the first layer{dot over (q)} _(AM-1) =αK _(AL)(T _(AM) −T ₁)

which is passed to the minuend input of a subtractor 68.

In the exemplary embodiment, the temperature dependence of the thermalconductivity λ₁ and the specific thermal capacity c₁ of the first layeris approximated by polynomials of the second degree, which arerepresented by coefficients W₀₁, W₁₁ and W₂₁ as well as C₀₁, C₁₁ andC₂₁. The polynomials used in the example have the following form:λ₁ =W ₀₁ +W ₁₁ T _(AM) +W ₂₁ T _(AM) ²c ₁ =C ₀₁ +C ₁₁ T _(AM) +C ₂₁ T _(AM) ²

This is replicated in terms of circuitry by the temperature of theworking medium T_(AM) being passed to the inputs of three multipliers70, 72 and 74. For the purpose of avoiding possible positive feedback(depending on the properties of the material) and consequently anincrease in the stability of the system, the forward-directed structureis used, i.e. the temperature of the working medium T_(AM) is usedinstead of the average temperature of the first layer T₁.

To calculate the thermal conductivity, the polynomial constant W₁₁ ispresent at the second input of the multiplier 70. The output isconnected to an input of an adder 76.

Present at the output of the multiplier 72 that is connected as asquarer is the signal for the square of the temperature of the workingmedium T² _(AM). It is multiplied by the polynomial constant W₂₁ bymeans of the multiplier 78 and subsequently passed to a second input ofthe adder 76.

The polynomial constant W₀₁ is switched to a third input of the adder76. Present at its output is the temperature-dependent thermalconductivity λ₁, given by the above expression.

To calculate the specific thermal capacity, the polynomial constant C₁₁is applied to the second input of the multiplier 74. The output of themultiplier 74 lies at an input of an adder 80. Present at a second inputof the adder 80 is the polynomial constant C₀₁. The square of thetemperature of the working medium T² _(AM) that is present at the outputof the multiplier 72 is provided with the polynomial coefficient C₂₁ bymeans of the multiplier 82 and is subsequently passed to a third inputof the adder 80. Present at its output is the temperature-dependentspecific thermal capacity c₁, given by the above expression.

The subtractor 84 forms the temperature difference from the averagetemperatures of the first layer and the following layer T₁−T₂. It ismultiplied by the temperature-dependent thermal conductivity λ₁, fromthe output of the adder 76, by means of the multiplier 86 and multipliedby the constant K_(W1), which includes the dependence on the layerthickness and the equivalent surface, by means of the multiplier 88.Present at the output of the multiplier 88 is the signal for the heatflow from the first layer into the second layer{dot over (q)} ₁₋₂=λ₁ K _(W1)(T ₁ −T ₂).

This signal is passed to the subtrahend input of the subtractor 68.Present at its output is the signal for the heat flow difference {dotover (q)}_(AM-1)−{dot over (q)}₁₋₂, which is provided by means of themultiplier 90 with a coefficient K_(T1), which allows for the rate ofchange of the temperature in the first layer in dependence on the weightof the material of the layer.

The resultant signal is divided by the signal that is present at theoutput of the adder 80 for the temperature-dependent specific thermalcapacity c₁ by means of a divider 92.

The average temperature of the inner layer is obtained by integration ofthe heat flow difference over time t

$T_{1} = {{\frac{K_{T\; 1}}{c_{1}}{\int_{0}^{t}{( {{\overset{.}{q}}_{{AM} - 1} - {\overset{.}{q}}_{1 - 2}} ){\mathbb{d}t}}}} + {T_{{Anf}\; 1}.}}$

The signal present at the output of the divider 92 is fed to anintegrator 94, which uses the initial temperature of the first layerT_(Anf1) as the initial condition.

The module for the second layer according to FIG. 4 determines theaverage temperature of the second layer T₂ from the transient heat flowbalance. For this purpose, the difference T₂-T₃ is initially formed bymeans of a subtractor 96 from the temperature of the third layer T₃ andthe average temperature of the second layer T₂ and multiplied by thetemperature-dependent thermal conductivity λ₂ of the second layer bymeans of a multiplier 98. A multiplier 100 provides the signal with asuitable coefficient K_(W2), which can be set and includes thedependence of the thermal conductivity on the layer thickness andsurface. Present at the output of the multiplier 100 is the signal forthe heat flow from the second layer into the third layer{dot over (q)} ₂₋₃=λ₂ W _(W2)(T ₂ −T ₃),

which is passed to the subtrahend input of a subtractor 102.

Present at the minuend input of the subtractor 102 is the signal for theheat flow {dot over (q)}₁₋₂ from the first layer into the second layer.Its input supplies the heat flow difference {dot over (q)}₁₋₂−{dot over(q)}₂₋₃. A multiplier 104 provides this signal with a coefficientK_(T2), which can be set and allows for the rate of change of thetemperature in the second layer in dependence on the weight of thematerial of the layer. Subsequently, the signal is divided by thetemperature-dependent specific thermal capacity c₂ of the second layerby means of a divider 106 and is then passed to the input of anintegrator 108. The integrator 108 uses the initial temperature T_(Anf2)of the second layer as the initial condition. Present at its output isthe average temperature of the second layer

$T_{2} = {{\frac{K_{W\; 2}}{c_{2}}{\int_{0}^{t}{( {{\overset{.}{q}}_{1 - 2} - {\overset{.}{q}}_{2 - 3}} ){\mathbb{d}t}}}} + {T_{{Anf}\; 2}.}}$

The temperature dependence of the thermal conductivity λ₂ and thespecific thermal capacity c₂ of the second layer is again approximatedby polynomials with coefficients W₀₂, W₁₂ and W₂₂ as well as c₀₂, c₁₂and c₂₂. The polynomials are:λ₂ =W ₀₂ +W ₁₂ T ₁ +W ₂₂ T ₁ ²c ₂ =C ₀₂ +C ₁₂ T ₁ +C ₂₂ T ₁ ²

This is replicated in terms of circuitry by the average temperature ofthe first layer T₁ being passed to the inputs of three multipliers 110,112 and 114. For the purpose of avoiding possible positive feedback(depending on the properties of the material) and consequently anincrease in the stability of the system, a forward-directed structure isused, i.e. the average temperature of the first layer T₁ is, usedinstead of the average temperature of the second layer T₂.

To calculate the thermal conductivity, the polynomial constant W₁₂ ispresent at the second input of the multiplier 110. The output isconnected to an input of an adder 116.

Present at the output of the multiplier 112 that is connected as asquarer is the signal for the square of the average temperature of thefirst layer T₁ ². It is multiplied by the polynomial constant W₂₂ bymeans of the multiplier 118 and subsequently passed to a second input ofthe adder 116. The polynomial constant W₀₂ is switched to a third inputof the adder 116. Present at its output is the temperature-dependentthermal conductivity λ₂, given by the above expression.

To calculate the temperature-dependent specific thermal capacity, thepolynomial constant C₁₂ is applied to the second input of the multiplier114. The output of the multiplier 114 lies at an input of an adder 120.Present at a second input of the adder 120 is the polynomial constantC₀₂. The square of the average temperature of the first layer T₁ ² thatis present at the output of the multiplier 112 is provided with thepolynomial coefficient C₂₂ by means of the multiplier 122 and issubsequently passed to a third input of the adder 120. Present at itsoutput is the temperature-dependent specific thermal capacity c₂, givenby the above expression.

The module for the third layer according to FIG. 5 determines theaverage temperature of the third layer T₃ from the heat flow balance.For this purpose, the temperature difference (T₃−T_(ISOL)) is firstformed by means of a subtractor 124 from the temperature of theinsulation T_(ISOL) and the average temperature of the third layer T₃and is multiplied by a suitable constant K_(ISOL), which can be set andrepresents the magnitude of the heat losses of the insulation, by meansof a multiplier 126. Present at the output of the multiplier 126 is thesignal for the heat flow from the third layer into the insulation (herethere is also the possibility of the heat losses of the insulation beingdirectly specified){dot over (q)} ₃ _(—) _(ISOL) =K _(ISOL)(T ₃ −T _(ISOL))

which is passed to the subtrahend input of a subtractor 128.

Present at the minuend input of the subtractor 128 is the signal for theheat flow {dot over (q)}₂₋₃ from the second layer into the third layer.Its input supplies the heat flow difference {dot over (q)}₂₋₃−{dot over(q)}₃ _(—) _(ISOL). A multiplier 130 provides this signal with acoefficient K_(T3), which can be set and allows for the rate of changeof the temperature in the third layer in dependence on the weight of thematerial of the layer. Subsequently, the signal is divided by thetemperature-dependent specific thermal capacity c₃ of the third layer bymeans of a divider 132 and is then passed to the input of an integrator134. The integrator 134 uses the initial temperature of the third layerT_(Anf3) as the initial condition. Present at its output is the averageintegral temperature of the third layer

$T_{3} = {{\frac{K_{W\; 3}}{c_{3}}{\int_{0}^{t}{( {{\overset{.}{q}}_{2 - 3} - {\overset{.}{q}}_{3 - {ISOL}}} ){\mathbb{d}t}}}} + {T_{{Anf}\; 3}.}}$

The temperature dependence of the specific thermal capacity c₃ of thethird layer is approximated by a polynomial with coefficients C₀₃, C₁₃and C₂₃.

The polynomial is:c ₃ =C ₀₃ +C ₁₃ T ₂ +C ₂₃ T ₂ ².

For the purpose of avoiding possible positive feedback (depending on theproperties of the material) and consequently an increase in thestability of the system, a forward-directed structure is used here, i.e.the average temperature of the second layer T₂ is used here instead ofthe average temperature of the third layer T₃.

This is replicated in terms of circuitry by the average temperature ofthe second layer T₂ being passed to the inputs of two multipliers 136and 138. The coefficient C₁₃ is applied to the second input of themultiplier 136. The output of the multiplier 136 lies at an input of anadder 140. Present at a second input of the adder 140 is the polynomialconstant C₀₃. The square of the average temperature of the second layerT₂ ² that is present at the output of the multiplier 138 is providedwith the polynomial coefficient C₂₃ by means of a multiplier 142 and issubsequently passed to a third input of the adder 140. Present at itsoutput is the temperature-dependent specific thermal capacity C₃, givenby the above expression.

According to FIG. 6, the average integral wall temperature T _(Int) isdetermined from the average temperatures of the individual layers T₁, T₂and T₃. Three multipliers 144, 146 and 148 provide the temperaturesignals with suitable weighting factors K_(G1), K_(G2) and K_(G3), whichweight the average temperatures of the individual layers in a waycorresponding to the weight of the material of the layer. The weightedtemperature signals pass to inputs of an adder 150. Its output signal isprovided with a coefficient K_(G), which allows for the influence of theoverall weight of the material of the equivalent portion of the wall, bymeans of a multiplier 152. Present at the output of the multiplier 152is the signal for the average integral wall temperature T _(Int).

1. A method for determining an integral average temperature in a wall ofa component, comprising: dividing the wall of the component into aplurality of layers; calculating an average temperature for each layerof the plurality of layers with allowance for the heat flow intoneighboring layers; and determining the average integral temperature inthe wall of the component using the average temperature for each of theplurality of layers in addition to using a plurality of measuredvariables, wherein the integral average temperature in the wall of thecomponent is determined without using temperature measuring points inthe wall.
 2. The method as claimed in claim 1, wherein the plurality ofmeasured variables includes a plurality of variables of a temperatureand a mass flow of a working medium flowing along the wall.
 3. Themethod as claimed in claim 2, wherein a steam throughput is determinedfrom a pressure and temperature of the working medium as well as a freevalve cross section.
 4. The method as claimed in claim 3, wherein a heattransfer coefficient for the heat transfer of the working medium intothe wall of the component in the case of exclusively superheated steamis determined as a function of the steam throughput.
 5. The method asclaimed in claim 3, wherein a heat transfer coefficient for the heattransfer of the working medium into the wall of the component in thepresence of condensation is determined in dependence on a condensationcomponent.
 6. The method as claimed in claim 5, wherein the averagetemperature of each layer is calculated from a transient heat flowbalance for the layer in question.
 7. The method as claimed in claim 6,wherein the temperature dependence of a thermal conductivity of eachlayer is approximated by a second degree polynomial.